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# 4.6 Completing the Square

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### 4.6 Completing the Square

1. 1. 4.6 COMPLETING THE SQUARE
2. 2. SOLVING BY FINDING SQUARE ROOTS <ul><li>Solving equations of the form </li></ul><ul><ul><li>Isolate the variable </li></ul></ul><ul><ul><li>“ Undo the Square” by taking the square root of both sides </li></ul></ul><ul><ul><li> Don’t forget: when you take the square </li></ul></ul><ul><ul><li> root your solution is ± </li></ul></ul>
3. 3. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
4. 4. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS
5. 5. EXAMPLE: SOLVE EACH EQUATION BY FINDING SQUARE ROOTS Note: No real number squared is equal to – 5, so the equation does not have a real number solution
6. 6. SOLVING A PERFECT SQUARE TRINOMIAL <ul><li>Remember that a perfect square trinomials are of the form: </li></ul><ul><li>Sometimes they can be set equal to a constant </li></ul>
7. 7. SOLVING A PERFECT SQUARE TRINOMIAL <ul><li>When a perfect square trinomial is set equal to a constant: </li></ul><ul><ul><li>Factor the trinomial </li></ul></ul><ul><ul><li>Take the square root of both sides </li></ul></ul><ul><ul><li>Solve for the value of the variable </li></ul></ul>
8. 8. EXAMPLE: SOLVE EACH EQUATION
9. 9. EXAMPLE: SOLVE EACH EQUATION
10. 10. COMPLETING THE SQUARE <ul><li>If is part of a perfect square trinomial, we can find a constant c so that is a perfect square trinomial. </li></ul><ul><li>This is a process called completing the square </li></ul>
11. 11. COMPLETING THE SQUARE <ul><li>We can form a perfect square trinomial </li></ul><ul><li> from by adding </li></ul>
12. 12. COMPLETE THE SQUARE <ul><li>Find the value of </li></ul><ul><li>Add the value to the expression, this completes the square </li></ul>
13. 13. EXAMPLE: COMPLETE THE SQUARE
14. 14. EXAMPLE: COMPLETE THE SQUARE
15. 15. SOLVING AN EQUATION BY COMPLETING THE SQUARE <ul><li>Rewrite the equation so it is of the form </li></ul><ul><li>Complete the Square: Add to both sides </li></ul><ul><li>Factor the prefect square trinomial </li></ul><ul><li>Take the square root of both sides </li></ul><ul><li>Solve for the variable </li></ul>
16. 16. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
17. 17. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
18. 18. EXAMPLE: SOLVE EACH EQUATION BY COMPLETING THE SQUARE
19. 19. HOMEWORK <ul><li>P 237 #1 – 8, 12 – 45 odd </li></ul>